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Equation solving

completing the square examples

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Algebra
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Completing the square
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Ex 2: f(x)= 7x2 +28x+56 o X1-F4(tsl' - - ? 510 71-J 2 +q)c -- (9'' H 84- x L +Lfx+ i F-4 = F( T *?g J?Z t r?q - = )C+z H Fx ?2? j Section 4-5: Solving with Completing the Square The Process 1) Set equation 0 2) Shove the constants to the other side 3) Get the Leading Coefficient to be 1 4) Complete the Square. Then add that value to both sides. 5) Take the square root of both sides and solve for x. For Examples 1-5 Find the solutions to the quadratic. Ex 1: f(x) = 3x2 + 42x + 24 0 3tL) 4- 2 ( - _ +r~ X Ex 3: g(x)=6x2 +6x+12 0 ('x 2. +LocW - xt / \ 1.- 2. - :+? - 9 '4 ( / X OL 0 Section 4-5: Solving with Completing the Square Ex4:y=x2 +7x+2 Ex5:f(x)=3x2 -12x+l O3x/yl

Absolute value notes

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Algebra
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Linear equation

1-4, 1-6 Solving Absolute Value Equations and Inequalities Absolute value: distance from zero on a number line. Since distance in a nonnegative, the absolute value of a number is always positive. The symbol lxi is used to represent the absolute value of a number x. I units 4 units I I I I 1 I 3 4 5 Solving Absolute Value Equations: For any real numbers a and b, where b ~! 0, if Jal = then a = b or ?a = b. The second case is often written as a = ?b. Steps 1. Isolate the Absolute Value expression 2. Rewrite equation without the I I symbols. a. One with positive answer b. One with negative answer Ex 1: Jx-51=7 x-c3- ?t-3 k'3 + 3. Solve each equation '7 2\: flL1 - '7 I 2 - \ - 4. Check your answers (plug back into I T

Algebra Fill In Notes 2.3

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02.03 Absolute Value Equations Essential Questions How can you represent constraints by absolute value equations? How can you interpret solutions as viable or nonviable options in a model? Absolute value equations can have: Examples One solution |x|= ________ Two solutions |x|= ______________________ No solutions |x| = _____________________ To solve an advance absolute value equation e.g. |2x-3|=11 Make two equations to solve by eliminating the absolute signs and making them equal opposite sign answers: Solve below: ___________________ ___________________ Check answers by substituting both into original equation. Check answers below: ____________________________________________ ____________________________________________ You can show constraints in real world problems by:

Algebra Fill In Notes 2.2

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02.02 Two-Variable Equations Essential Questions How can we create equations in two or more variables to represent relationships between quantities? How can we represent constraints by equations or inequalities and interpret solutions as viable or nonviable options in the model? Main Idea (page #) DEFINITION OR SUMMARY EXAMPLE Two-Variable Equations p.2 Steps to solving problems Read and understand the situation within the word problem. Identify and pull out ______________ ______________ from the problem. Assign ____________to unknown values. Set up and solve the equation. Check that your answer makes sense within the context of the problem. Consecutive integer problems p.2 Label the first integer with x, the next with x + 1, the next with x + 2, and so on.

Algebra Help

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Algebra

Applying the Fundamental Concepts of Algebra An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. For engineers and scientists it is an essential requirement. The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here. USING REAL NUMBERS
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